Pressure sensor element and method to measure contact stress

ABSTRACT

A biological implantable pressure sensor element comprises a fixed volume pouch formed by a sealed, flexible, impermeable membrane comprising therewithin a gel mass contained in a gel volume, said gel being hydrated with an aqueous solution comprising an agent having at least a first and a second NMR-detectable form, the proportion of the first to the second form of the agent in the gel volume being determined by their electrolytic interaction with the gel, whereby when an external pressure is applied to the sensor element a d (chemical shift)/d(σ/K) greater than 0.0001 ppm is attained, wherein σ is the external pressure and K is the modulus of the gel. A kit contains sterile, individually wrapped sensor elements. 
     A method of measuring in vivo contact stress applied to an implanted pressure sensor element, comprises implanting the pressure sensor of the invention into a situs of a subject in need of such measurement, non-invasively subjecting the subject situs to a nuclear magnetic resonance source effective to detect said NMR-detectible agent, obtaining the NMR spectrum of said agent, obtaining the chemical shifts from the spectrum, repeating steps (b) to (d) at least once at a desired time interval, comparing the chemical shifts obtained in step (d) at different time intervals, and calculating the contact stress applied to said sensor element at a desired time from a correlation of observed chemical shifts for normalized stresses (σ/K) for the sensor element. 
     A method of measuring in vitro contact stress applied to a pressure sensor element, comprises placing the stress sensor element of the invention in contact with a biological tissue in culture, non-invasively subjecting the biological tissue to a nuclear magnetic resonance source effective to detect said NMR-detectible agent, obtaining the NMR spectrum of said agent, obtaining the chemical shifts from the spectrum, repeating steps (b) to (d) at least once at a desired time interval, comparing the chemical shifts obtained in step (d) at different time intervals, and calculating the contact stress applied to said sensor element of a desired time from a correlation of observed chemical shifts to normalized stresses (π/K) for the sensor element.

This application is a Continuation application of application Ser. No.07/535,616, filed Jun. 11, 1990 now abandoned, which is a divisionalapplication of application Ser. No. 07/261,303, filed Oct. 24, 1988 U.S.Pat. No. 4,967,764.

BACKGROUND OF THE INVENTION

This invention relates to an implantable pressure sensor elementutilizing non-invasive NMR spectroscopy as a measuring tool. The sensorelement requires no external connections and releases no toxicsubstances into the host system. The sensor element may be utilized forthe in vitro as well as in vivo measurement of the normal component oftissue stress. The present invention finds its use in numerousapplications among which are medical applications and biotechnologyapplications.

Elevated levels of mechanical stress may induce tissue trauma byreducing perfusion or compromising structural integrity. When tissue iscompressed such as when a growing tumor displaces the tissue, thecapillary volume in the region is reduced. This, in general, causes aconcomitant reduction in blood perfusion to the area. Additionalcompression may cause the development of nerve pinching, microtears andother structural defects. If the capillary pressure increases while thesurrounding tissue is confined by rigid or indistensible walls traumamay also result. A good example of the latter is the case of cardiac orbrain edemas where increased fluid volume occurs at the expense ofdecreased tissue volume. Either condition may cause damage to vitalbiological structures. This is also true of stresses applied to otherparts of the human body. The stress developed within the tissue thatcauses this damage is called the mechanical contact stress. Contactstress is defined as the normal component of the interfacial stressbetween two bodies It should be remarked that contact stress within thecontext of this invention is not the hydrostatic pressure.

In situations where the monitoring of pressure is necessary such asthose encountered in the biomedical arts it is desirable to have adevice which is entirely implantable within the body of the subject.Many prior art devices provided for this purpose are transcutaneous,that is, a portion of the device extends outside of the subject's body.These devices have the drawback that they have a high incidence ofinfection at the point where the device emerges from the subject's body.In addition, in many instances cables emerging from the subject's bodylimit the mobility of a patient (e.g., U.S. Pat. Nos. 4,660,568,4,246,908, 4,393,878, 4,186,749 and 4,738,267, French Patent Nos.2,455,735, 2,384,482, 2,274,261 and 2,262,953 and German Patent No.1,965,231, among others).

Other prior art devices are known which are fully implantable and do notrequire any connectors to emerge through the skin of a subject's body.These devices are implantable electronic devices which are interrogatedby induction or which transmit coded information to an appropriatemonitor. In many instances they contain complex precision electronicequipment which must be implanted, e.g., inside the head of a subject,and require high expenditures, and sophisticated monitoring apparatuses(e.g., U.S. Pat. Nos. 3,977,391, 4,124,023, 4,006,734, 3,911,902 and2,566,369, among others).

Other devices are also known which utilize radiopaque materials whichare mechanically shifted in proportion to changes in pressure once thedevice is implanted. One such example is the X-ray opaque devicedescribed in U.S. Pat. No. 4,627,443. Another such device is describedin U.S. Pat. No. 4,660,568. This patent provides an intracranialimplantable sensor which undergoes a conformational change with pressureand is coupled through the skin by electromagnetic, acoustic ormechanical transmission to an external device which detects the changeand interprets the pressure. This sensor has an insulating body with amoveable element which oscillates along an opening or channel in thebody of a subject. The element communicates with the externalatmospheric pressure by means of a membrane which is nearly coplanarwith the intact skin covering it and on the other side with the internalpressure by another membrane. The degree of the moveable element'sdisplacement relative to the body of the subject is correlated with thedifference in the internal and atmospheric pressures.

A further type of implantable pressure sensor element is that providedby U.S. Pat. No. 3,958,562. This sensor element comprises a siliconerubber vessel, the walls of which have wax trapped therewithin, which isfilled with a non-toxic hydraulic fluid compatible with body fluidsHowever, this pressure sensor has attached thereto a piece oftranscutaneous tubing for conducting out displaced liquid which mayoperate as a bellows.

A further implantable device is that described in U.S. Pat. No.4,340,038 which operates as a magnetic field concentrator and mayfunction for instance as an intracranial pressure monitoring device. Theimplanted sensor has a magnetic field pick-up which when placed next toan external magnetic field generator is capable of converting magneticenergy to electrical energy for energizing the device. The devicecontains a ferrite material and is adapted to operate in response toenergy provided by an externally located magnetic field generator.

Thus, there is still a need for further development of biocompatibleimplantable devices which are capable of fast measuring of contactpressure by non-invasive means.

SUMMARY OF THE INVENTION

This invention relates to a biological implantable contact pressuresensor element comprising a fixed volume pouch formed by a sealed,flexible, impermeable membrane comprising therewithin a gel masscontained in a gel volume, said gel being hydrated with an aqueoussolution comprising an NMR-detectable agent, whereby when an externalcontact pressure is applied to the sensor element a d(chemicalshift)/d(σ/K) greater than about 0.0001 ppm is attained, wherein σ isthe external contact pressure and K is the modulus of the gel.

A kit is also part of the invention comprising preferably 1 to 100sensor elements in accordance with the invention, which may besterilized and individually wrapped.

This invention also relates to a method of measuring in vivo contactstress applied to an implanted pressure sensor element comprising:

(a) implanting the pressure sensor of this invention into a situs of asubject in need of such measurement;

(b) non-invasively subjecting the subject situs to a system capable ofmeasuring the nuclear magnetic resonance spectrum of said NMR-detectibleagent;

(c) obtaining the NMR spectrum of said agent;

(d) obtaining the chemical shifts from the spectrum;

(e) repeating steps (b) to (d) at least once at a desired time interval;

(f) comparing the chemical shifts obtained in step (d) at different timeintervals; and

(g) calculating the contact stress applied to said sensor element at adesired time from a calibration curve relating observed chemical shiftsto the normalized stress (σ/K) for the sensor element.

Also part of the invention is a method of measuring in vitro contactstress applied to a pressure sensor element, comprising

(a) placing the stress sensor element of the invention in contact with abiological tissue in culture;

(b) non-invasively subjecting the biological tissue to a system capableof measuring the nuclear magnetic resonance spectrum of saidNMR-detectible agent;

(c) obtaining the NMR spectrum of said agent;

(d) obtaining the chemical shifts from the spectrum;

(e) repeating steps (b) to (d) at least once at a desired time interval;

(f) comparing the chemical shifts obtained in step (d) at different timeintervals; and

(g) calculating the contact stress applied to said sensor element at adesired time from a calibration curve relating observed chemical shiftsto the normalized stress (σ/K) for the stress element.

A more complete appreciation of the invention and many of the attendantadvantages thereof will be readily perceived as the same becomes betterunderstood by reference to the following detailed description whenconsidered in connection with the accompanying figures.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 shows a sensor element in accordance with the invention whichconsists of an impermeable but flexible pouch containing apolyelectrolyte gel bathed in an aqueous solution.

FIG. 2 shows the functional relationship between interstitial andexternal pH of the aqueous solution and an applied stress onto thesensor element. This is an "equilibrium stress titration curve" whichshows the close analogy between chemical and mechanical titration. Anequilibrium results between the internal and external gel pH from slowlyincreasing the applied stress on the sensor element. The value of thestress applied is normalized by dividing the stress by the bulk modulusof the gel (σ/K, which is dimensionless).

FIG. 3 depicts the stress sensitivity of a sensor element in accordancewith the invention. In the figure the variation of the pH with thenormalized stress in the interstitial and external gel fluid volume canbe seen. The sensitivity of the sensor element can be calculated bytaking the derivative of the pH v. σ/K curve with respect to thenormalized stress.

FIG. 4 shows the variation of the chemical shift of the NMR-detectableagent present in the sensor device in accordance with the invention withpH variations in the external solution and/or the gel volume within thedevice.

FIG. 5 shows a test device built in accordance with the presentinvention. The end of a 20 cm³ plastic syringe is sealed with paraffintape. Holes are drilled through its rubber tamper so that fluid can flowthrough it when the plunger is depressed. The syringe is filled with geland the indicator solution and then placed in an RF coil in the core ofthe magnet. Initially, no compressive force is applied to the plunger.Fluorine and proton NMR spectra are obtained. The same sample is thensubjected to an applied compressive force of approximately 1.0 Newton ora calculated mean stress of 0.32 N/cm². The gel is allowed toequilibrate for about 1 hour prior to performing a second measurement.The total volume of polymer and solvent is maintained constant in bothexperiments as it is in the sensor element.

FIG. 6A shows the proton spectrum of the uncompressed sensor element andFIG. 6B shows the proton spectrum of the compressed sensor element.

FIG. 7 shows the fluorine NMR spectrum of the uncompressed sensorelement shown in FIG. 5.

FIG. 8 shows the fluorine NMR spectrum of the compressed sensor elementdescribed in FIG. 5.

The split peaks observed in the spectra of FIGS. 7 and 8 arecharacteristic spectra lines of the fluorine moiety. However, thechanges in the relative spacing between peaks does reflect a change inthe pH of the interstitial and external solutions.

Other objects, advantages and features of the present invention willbecome apparent to those skilled in the art from the followingdiscussion.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention arose from a desire by the inventor to provide anovel sensor element in vivo as well as in vitro methods of measuringcontact stress which were fully implantable, needed no externalconnectors and are inexpensive and easy to monitor and provide accuratecontact stress measurements.

Thus, although the sensor element of this invention must be firstimplanted for conducting the in vivo measurements, it requires noexternal connections for its continued operation unlike other commonstress or strain transducers. The stress applied to the sensor elementis determined by a non-invasive NMR spectroscopic method. In fact, thegel contained in the sensor element may be viewed as a passive telemetrysystem which transmits its dilation to a remote receiver coil upon beinginterrogated by an RF pulse. The sensor may be sterilized prior toimplantation to ensure full sterility. However, the absence of leads orwires emerging from the patient after the sensor element is implantedensures extremely high probabilities of maintaining a sterile fieldtherearound. The sensor element of this invention measures anequilibrium mechano-chemical effect, and accordingly an excellent DCresponse is attained. Moreover, the sensor contains no cytotoxicsubstances or non-toxic chemicals whose release would present a threatto the surrounding biological tissues. The operating range andsensitivity of the sensor can be varied by a careful selection of theelements utilized in the manufacture of the sensor element itself. Forinstance, the composition of the gel and its physical and chemicalproperties (e.g., its stiffness, degree of cross-linking and relativeamount of monomer components) may be varied to suit the needs of aparticular application. In addition, the NMR-detectable agent utilizedis not an endogenous substrate and can be easily detected since thetissues surrounding the implanted sensor element are NMR-transparent forthe most part. Thus, very low background signal noise is encountered.

This invention provides a biological implantable pressure sensor elementcomprising a fixed volume pouch formed by a sealed, flexible,impermeable membrane comprising therewithin a gel mass contained in agel volume, the gel being hydrated with an aqueous solution comprisingan agent having at least a first and a second NMR-detectable form, theproportion of the first to the second form of said agent and said gelvolume being determined by their electrolytic interaction with the gel,whereby when an external pressure is applied to the sensor element ad(chemical shift)/d(σ/K) greater than about 0.0001 ppm, and morepreferably greater than about 0.01 ppm and still more preferably about0.1 to 10 ppm, is attained, whereby σ is the external pressure and K isthe modulus of the gel.

In a separate embodiment the gel mass can be surrounded by a softer,neutral or electrolyte gel and/or the NMR-detectable agent may be partof the polymeric structure of the gel.

The sensor element may be manufactured in any desired size and suited tothe particular application it is intended for. Accordingly, if it is tobe implanted in a small part of the human body it may be provided in asize ranging in diameter from about 0.01 to 1000 cm³. For areas that arelarger and can accommodate a larger device the sensor element may have adiameter of about 1000 to 10000 cm³. The sensor element for utilizationin vitro may be manufactured in any desired size and shape thus beingadaptable for specific applications. One such example may be the sensorelement of the invention being manufactured in a cylindrical form of arather large circular diameter which could be used as the support forthe growth of cells. Accordingly any size in which cell tissues arecustomarily manufactured are appropriate for the present sensor element.The same is true in terms of the shape of the sensor element for in vivoimplantation. The element may be manufactured in any shape suitable toaccommodate the implantation requirements of specific body sections.

In an embodiment exemplified in this patent, the NMR-detectable agent isa ¹⁹ F compound. However, other NMR-detectable compounds may be utilizedas suitable. Examples of compounds known at the present time are ¹⁹F-trifluoroethylanine, ³¹ phosphoric acid and ¹³ C-carbonic acid.However, other NMR-detectable agents are being manufactured al the timewhich provide higher sensitivity and more accurate measurements andthose can be utilized as they become known.

In a particular embodiment of the present invention the NMR-detectableagent is charged. Suitable agents are weak acids and bases such as aminoacids. However, other electrolytes may also be utilized which may or maynot be physiologically acceptable since the agent is not placed indirect contact with body tissues. Examples of electrolytes suitable foruse with the present invention are fluorinated amino acids such asdifluromethylalanine, and the like.

FIG. 1 depicts a sensor element in accordance with the present inventionwhich consists of an impermeable but flexible pouch containing apolyelectrolytic gel bathed in an aqueous solution. In operation, stress1 is applied to a tissue 2. Tissue 2 is in contact with a sensor elementin accordance with the invention shown to consist of a flexible membrane3, containing an external bath 4, and a gel mass 5. The sensor is shownin the figure to be in touch with a tissue 6 which may in turn besubjected to stress 7 from the opposite side.

FIG. 5 shows a test device built in accordance with the presentinvention. The end of a 20 cm² plastic syringe 8 is sealed with paraffintape. Holes 13 are drilled through the rubber tamper 12 of the syringeso that fluid can flow through the tamper when the plunger 9 of thesyringe is depressed. The syringe is filled with gel 14 and theindicator solution or external bath 11 and then placed in an RF coil inthe core of a magnet. Valves 14 connect tubes a and b to the interior ofthe syringe(s) and allow for remote control of pressure withoutmanipulation of the plunger 9.

The pouch of the sensor element is formed of a sealed membrane which isflexible and impermeable. Suitable membrane materials are polyethylene,urethane and polyurethane, among others. However, other materials havingthese characteristics are known in the art and are also suitable formanufacturing the present device. In a particularly useful embodiment ofthe sensor element of the invention for in vivo utilization the membranecomprises a non-biodegradable, physiologically-acceptable membranematerial. However, other materials having similar characteristic mayalso be utilized herein.

The gel of the sensor element of the invention may be formed from amonomer by polymerization and/or crosslinking thereof. Typically, apolymerizable monomer is selected and various polymerization and/orcrosslinking degrees are tested in order to obtain a gel having thedesired modulus characteristics. A suitable material for the gel ispolyacrylamide. Once polymerized and/or crosslinked, the polymers may bepartially degraded and/or hydrolyzed in order to attain the desiredcharge density characteristics thereof. Suitable gel materials arepartially hydrolyzed polyacrylamide, and the like. However, othermaterials having similar characteristics may also be utilized.

Although the sensor element of the invention may be manufactured in avariety of forms, shapes and consistencies, a generally suitable deviceis that where a proportion of gel:solution in the pouch is about 1:10 to10:1, more preferably about 1:8 to 8:1, and still more preferably about1:5 to 5:1. Also, in general the NMR-detectable agent is present in theaqueous solution contained in the touch in an amount of about 1×10⁻⁵ to3.0M, and preferably about 5.0×10⁻³ to 1×10⁻² M. However, otherconcentrations of the NMR-detectable agent may be utilized as suitablefor optimal detection taking into consideration the distance between theimplantation site and the NMR source and detector as well as the loss ofsignal due to the implantation depth.

The sensor element comprises an impermeable but flexible pouch thatcontains a gel in an ionic solution. However, other ions may be presentin the aqueous solution and as pH defining ions and the like and asofter gel may surround the central gel core. FIG. 1 shows a schematicdiagram of the pouch, the external solution and the gel.

One embodiment of the invention is set forth in the examples. The gelused in the examples is hydrolyzed polyacrylamide that is hydrated in anaqueous cocktail (pH 7.5) containing Na⁺, Cl⁻ anddifluoromethylalanine-hydrochloride as the NMR-detectable agent. Thelatter is a sensitive pH indicator used to measure intercellular andintracellular pH in vivo with ¹⁹ F NMR spectroscopy. The charged groupson the polymeric backbone of the gel are ionized at pH 7.5. Thus, theequilibrium concentration of the mobile ions, e.g., ([Na⁺ ], [OH⁻ ], [H⁺], [Cl⁻ ], and the two charged species of the ¹⁹ F NMR indicator, [NH⁺ ₃C(CH₃)CHF₂)COOH] and [NH₂ C(CH₃)(CHF₂)COO⁻ ], differ in the interstitialand external fluid compartments.

When a normal stress applied to the bag compresses the gel, fluid issqueezed from this sponge-like material into the surrounding bath. Thisdecreases the volume of interstitial fluid and increases the chargedensity of the charged groups on the gel. A redistribution of the mobileco- and counter-ions, including H⁺, between the interstitial andexternal volumes is eventually achieved. The new equilibrium isreflected by, in this case, a change in pH of the interstitial andexternal volumes.

In other embodiments of the present invention the NMR-detectable agentmay be sensitive to solution parameters affected by the gel other thanpH, such as other ionic entities and the like. However, these parametersmust undergo changes which are attributable to the contact pressureexerted on the device. These changes are detectable by measuring, e.g.,the chemical shift or other characteristics, in the NMR spectrum of theindicator molecule or NMR-detectible agent. The change in chemical shiftis herein related to the applied stress by a mathematical modeldescribed below or an empirically derived relationship between thechemical shift and applied stress provided herein.

Mathematic Model of the Sensor's Response to an Applied Stress

The present mathematical model attempts to relate the applied stress tothe measured shift in the ¹⁹ F NMR spectrum of the sensor. Continuummechanics is used to describe the behavior of the gel under loadingwhile physical-chemistry is used to determine the chemical changes thatthese stresses induce. Finally, elementary quantum mechanics is used todetermine how these chemical changes affect the frequency shifts in the¹⁹ F NMR spectra. More specifically, an equation of the conservation ofmomentum and a constitutive law of the gel, with appropriate boundaryconditions, expresses as the relationship between the applied stress andthe dilatation of the gel. The equations of conservation of mass,electroneutrality, electrochemical equilibrium and equilibriumdissociation of each chemical species constitute the description of thechemical interactions between the gel and the external bath. Theseexpressions can be simplified to a system of non-linear algebraicequations that a re solved numerically for the parameter, e.g., thehydrogen ion concentrations, within the gel and in the external bath.Finally, equations that relate the shift in Larmor frequencies of theobserved ¹⁹ F NMR spectrum to the degree of dissociation of theparameter indicator or NMR-detectible agent, e.g., pH indicator,complete the model.

The polymer network is assumed to satisfy the constitutive law of anisotropic, Hookean material in accordance with the following equation.##EQU1## wherein K is the bulk elastic modulus of the gel and G is itsshear elastic modulus. For small deformations, the strain tensor,ε_(ij), is defined as ##EQU2##

Since the gel is assumed to be in mechanical equilibrium, theconservation of linear momentum of the gel takes the following form.##EQU3##

If the gel is assumed to be in the shape of a rectangular prism when auniform compressive stress,-σ₀, is applied on two of its faces while theother four faces are stress-free and unconstrained the applied stresscan be related to the dilatation of the sample by the followingequation.

    -σ.sub.0 =3 Kε

wherein ε is the dilatation, ε=ε_(xx) +ε_(yy) +_(zz). For smalldeformations, this quantity is equal to the fractional change in gelnetwork volume relative to its unstrained state that is produced by theapplied stress obtained from the following equation. ##EQU4## wherein Vis the volume of gel in the deformed state and V₀ is the is the volumein the undeformed state.

Using equations 2 and 3 together, we can relate the stress applied tothe gel can be related to its volume as follows. ##EQU5##

If the bulk modulus and the dilatation of the gel are known, equation 3ahelps to calculate the magnitude of the compressive stress applied tothe gel. It should be noted that equation (3a) is only valid for smalldeformations.

A mathematical relationship between the dilatation of the sample and theresultant chemical shift of an indicator molecule determined by ¹⁹ F NMRare derived hereinbelow.

The sensor element of the invention is modeled as two compartments thatare in electrochemical equilibrium with one another. One compartment isthe gel polymer network and its interstitial fluid and the other is theexternal solution contained in the pouch. Both compartments are enclosedby a flexible, indistensable membrane pouch that is impermeable to waterand other ions but allows heat to be exchanged across its walls. Thispouch is assumed to lie in an infinite temperature reservoir.

Since no matter is exchanged across the impermeable barrier, theequation of the conservation of mass of each species within the bagtakes the following form. ##EQU6## wherein M_(i) is the moles of thei^(th) constituent molecule, [C_(i) ]_(j) is the concentration of thei^(th) constituent molecule in the j^(th) compartment, V_(j) is thevolume of the j^(th) compartment and N_(c) (2 in this case) is the totalnumber of compartments. Since the number of moles of each species insolution is prescribed by the artisan, all of the M_(i) can be treatedas constants in the model. As such, equation (4a) constitutes a set ofconstraint equations.

An additional constraint equation is provided when the condition thatthe contents of the pouch are individually incompressible is applied sothat the total volume of the sensor, V_(T), remains constant as can beseen from the following equation. ##EQU7##

The condition of macroscopic electroneutrality in each compartmentimposes yet another constraint. If Z_(i) is the valence number of thei^(th) constituent molecule and N_(j) is the total number of chargedspecies present in compartment j, then ##EQU8##

Although this discussion is restricted to a two-compartment system,these formulas can be extended to model multi-compartment systems aswell It is herein assumed that the sensor is in thermodynamicequilibrium and there is no net flux of water or ions betweencompartments. Under these conditions the Folker-Plank equation resultsin the well-known Donnan equilibrium equations (5). ##EQU9## where i andk denote any two mobile ionic species.

The carboxylic acid groups that are covalently bonded to the backbone ofthe exemplary gel are modeled as a monoprotic weak acid, HP, whosedissociation is governed by the following chemical formula.

    HP+H.sub.2 O<=>H.sub.3 O.sup.+ +P.sup.-

where [P⁻ ] is the concentration of ionized groups in the interstitialsolvent. The weak acid obeys the following equilibrium dissociationrelationship ##EQU10## wherein K_(a) ' is the acid dissociationconstant.

The total concentration of ionizable groups, [P_(tot) ], is therefore

    [P.sub.tot ]=[P.sup.- ]+[HP].                              (5b)

By combining equations (5a) and (5b) it is possible to express theconcentration of ionized or fixed-charges in terms of the hydronium ionconcentration [H₃ O⁺ ] and the total concentration of ionizable groupsin the network as follows. ##EQU11##

Moreover, as the total number of ionizable groups in the polymer isconserved, equation (4a) becomes:

    M.sub.P.sbsb.tot =V.sub.2.sbsb.0 [P.sub.tot ].sub.0 =V.sub.2 [P.sub.tot ]

wherein V₂.sbsb.0 is the volume of the gel in its undistended state and[P_(tot) ]₀ is the corresponding concentration of ionizable groups whenthe applied stress is zero. The dissociation of water is also requiredto obey the following familiar equation.

    [H.sub.3 O.sup.+].sub.1 [OH.sup.- ].sub.1 =K.sub.W '=[H.sub.3 O.sup.+ ].sub.2 [OH.sup.- ].sub.2                                 (7)

For the particular chemical system used in the exemplary tests, theequations of electroneutrality become

    [ H.sub.3 O.sup.+ ].sub.1 +[Na.sup.+ ].sub.1 +[NH.sub.3.sup.30 --R--COOH].sub.1 -[OH.sup.- ].sub.1

     -[Cl.sup.- ].sub.1 -[NH.sub.2 --R--COO.sup.- ].sub.1 =0   (8)

for compartment 1, and

    [ H.sub.3 O.sup.+ ].sub.2 +[Na.sup.+ ].sub.2 +[NH.sub.3.sup.+ --R--COOH].sub.2 -[OH.sup.- ].sub.2

     -[Cl.sup.- ].sub.2 -[NH.sub.2 --R--COO.sup.- ].sub.2 -[P.sup.- ]=0 (9)

for compartment 2.

Because indicators are usually present in trace concentrations, theireffect is often neglected in typical acid/base calculations. Sincemillimolar concentrations of indicator or NMR-detectible agent may beused to improve the signa/noise ratio of the spectroscopic measurementits dissociation reactions must also be included in this model.

Once dissolved in solution, the amphoteric ¹⁹ F NMR indicatordissociates in a two-step reaction which may be described as follows.##STR1##

The total number of moles of indicator is then

     M.sub.ind =V.sub.1 ([NH.sub.3.sup.+ --R--COO.sup.- .sub.1 +[NH.sub.3.sup.+ --R--COOH].sub.1 +[NH.sub.2 --R--COO.sup.- ].sub.1)

     + V.sub.2 ([ NH.sub.3.sup.+ --R--COO.sup.- ].sub.2 +[NH.sub.3.sup.+ --R--COOH].sub.2 +[NH.sub.2 --R--COO.sup.- ].sub.2)

The electrically neutral Zwitterion, NH₃ ⁺ --R--COO⁻, is a smallmolecule that can move freely between compartments At equilibrium it isassumed to be present in equal concentrations in each compartment:

    [NH.sub.3.sup.+ --R--COO].sub.1 =[NH.sub.3.sup.+ --R--COO.sup.- ].sub.2.

After various substitutions, equations (8) and (9) can be placed in thefollowing forms.

    h.sub.1 ([H.sub.3 O.sup.+ ].sub.1, [H.sub.3 O.sup.+ ].sub.2)=0 (10)

    h.sub.2 ([H.sub.3 O.sup.+ ].sub.1, [H.sub.3 O.sup.+ ].sub.2)=0 (11)

wherein h₁ and h₂ each are scalar functions whose exact form is givenbelow. These two equations now contain only two dependent variables, [H₃O⁺ ]₁ and [H₃ O⁺ ]₂. The other quantities are either independentvariables that can be prescribed by the artisan or material constantswhose values are known a priori by independent measurements. The stressis treated as a free parameter. Therefore, equations (10) and (11)constitute a system of two non-linear, algebraic equations with twounknowns which can be solved using standard numerical techniques, suchas the Levenberg algorithm Numerical routines used to solve a system ofnon-linear algebraic equations are provided in the IMSL Library ofScientific Subroutines, Version 1.0, IMSL, Houston, Tex.; "NumericalRecipes" by Press, Flannery et al, Cambridge Press (1986).

A similar treatment may be applied to obtain a change in a parameterother than pH which is caused by contact pressure applied to the sensorelement of the invention. FIG. 2 shows the calculated relationshipbetween the parameter in, e.g., pH, in both the external and internalbath and the normalized applied stress. The stress, σ, is normalized bythe bulk modulus of the gel, K, therefore making the ratio, σ/K,dimensionless. This figure is aptly titled "stress titration curve"because of the close analogy that exists between mechanical and chemicaltitration experiments It shows the predicted equilibrium interstitialand external solution parameter, e.g., pH, that would result fromincreasing the applied stress on the gel reversibly (i.e., maintainingthe system in electromechanochemical equilibrium). The difference in theparameter, e.g., pH, between the interstitial and external solutions atequilibrium is obtained from the Donnan equations.

The sensitivity of the gel sensor element is given by the slope of theparameter, e.g., pH, vs. σ/K curve. It is calculated by numericallydifferentiating the curves of the parameter, e.g., pH, vs. σ/K curvewith respect to σ/K using a centered differences formula. The resultsare shown in FIG. 3. In the expected operating range of the exemplifiedsensor (i.e., σ/K<about 1) its sensitivity is approximately 0.25 pHunits per unit change in the normalized stress. The sensitivity andrange of the gel are controlled by several independent variables: thepolymer content, the degree of crosslinking, the number of ionizablegroups and the bulk modulus, K, among others.

The equations given above can be used to determine the applied stressfrom the gel interstitial and external concentrations of any of themobile ionic species. Such measurements can be performed using ionselective electrodes or colormetric indicators, for example. In order todetermine these concentration differences using ¹⁹ F NMR spectroscopy,another relationship must be derived between the chemical shift observedin the ¹⁹ F NMR spectrum and the concentration of mobile ions withineach compartment of the sensor. Determination of the ¹⁹ F NMR ChemicalShift from the Distribution of [H₃ O⁺ ]₁ and [H₃ O⁺ ]₂ ]:

The indicator, a difluorinated amino acid, can exist in one of threedissociation states. It will be shown that the relative population ofeach state reflects the ambient pH. Since the chemical shift differs foreach state, the measured chemical shift is shown to be predictablyrelated to pH.

The lifetime of a particular is on the order of its inverse dissociationrate constant whereas the time it precesses in the magnetic field equalsits inverse Larmor frequency. The rate constant of dissociation isproportional to exp(-ΔG*/kT) where ΔG* is the activation energy of thestate, k is the Boltzmann constant and T is the absolute temperature.For the deprotonation reaction of an amine group, the rate constant˜O(10⁶) Hz. However, the relevant frequency of the acquistion of thespectrum is (ν_(a) -ν_(b))/2 where ν_(a) and ν_(b) are the Larmorfrequenciesν of one of the Fluorine moieties in the protonated anddeprotonated states, respectively. For this indicator, this frequencydifference is O(10²) Hz. Therefore, the indicator changes its state anaverage of 1000 times during the time an individual ¹⁹ F NMR spectrum isacquired. In this rapid exchange limit, the measured chemical shiftspectrum of each dissociation state of the indicator molecule, i,weighed by its probability of occurrence, p(i)₁. The indicator used inthese experiments exhibits three separate dissociation states, so thechemical shift is given as:

     E(I.sub. 1,I.sub.2,I.sub.3 I.sub.4).sub.1 =p(0).sub.1 (I.sub. 1,I.sub.2,I.sub.3,I.sub.4).sub.1.sup.(0) +p(-1).sub.1 (I.sub. 1.sub.,I.sub.2.sub.,I.sub.3, I.sub.4).sub.1.sup.(-1)

     +p(+1).sub.1 (I.sub. 1.sub., I.sub.2, I.sub.3,I.sub.4).sub.1.sup.(+1) (11a)

The components of the vector, (I₁, I₂, I₃, I₄)₁ represent the peaks ofthe four chemical shift lines (Hz) which comprise the quartet observedin the ¹⁹ F NMR spectrum. Since the measured chemical shift is shown tobe a mathematical expectation it is denoted as E(I₁, I₂, I₃, I₄)₁. Theprobability of a particular state, i, is just its relative concentrationin solution: ##EQU12## Therefore, the measured chemical shift can beexpressed in terms of the chemical shift of the different states of theindicator and their respective relative concentrations: ##EQU13## Ananalogous expression can be written for the second compartment that iscommunicating with the first: ##EQU14##

It has been observed that the measured difference, E(I₂ -I₃), issensitive to pH changes. A formula for this difference signal isobtained from equation (20): ##EQU15##

FIG. 4 shows the calculated values of I₂ -I₃ (ppm) plotted against pHfor both the external and interstitial solutions The relativeconcentrations of the indicator were obtained from equations 13 and 14.Once the hydronium ion concentration is known in both compartments, theconcentration of each of the indicator species was determined usingequations 12a-d. In preparing FIG. 4, values of I₂ -I₃ in theZwitterionic and negatively charged states were estimated from Deutschet al. In the pH range at which the sensor is maintained, the indicatorexists primarily in the Zwitterionic and negatively charged forms sothat the last term in equation (20a) could be neglected.

In the operating range of this sensor element, the indicator existsprimarily in the Zwitterionic and negatively charged form states.Therefore, the last terms in equations 12 and 13 can be neglected.

The time it takes for the indicator to diffuse between compartmentsscales with δ² /D where δ is a characteristic length and D is thediffusivity of the indicator molecule in water. For this sensor elementD ˜0.9×10⁻⁵ cm² /sec²⁰ and δ ˜0.1 cm so that δ² /D˜1000 sec. Since thediffusion time is much greater than 2/(ν_(a) -ν_(b)) ˜0.01 sec, it canbe assumed that the indicator molecules will remain in their respectivecompartments while the spectrum is measured. This implies that thespectrum from a two-compartment system will be the superposition of thespectra from each compartment. Since the strength of the signal isproportional to the mass of the indicator, the measured spectrum will beproportional to the spectra from compartments 1 and 2 weighted by theirrespective volumes:

    (I.sub.1,I.sub.2,I.sub.3,I.sub.4).sub.m ˜[IND.sub.tot ].sub.1 V.sub.1 (I.sub.1,I.sub.2,I.sub.3,I.sub.4).sub.1 +[IND.sub.tot ].sub.2 V.sub.2 (I.sub.1,I.sub.2,I.sub.3 I.sub.4).sub.2                   (14)

FIG. 7 illustrates this last point It shows a typical measured ¹⁹ F NMRspectrum of the gel and the external bath The two distinct quartets,marked i and o (standing for interstitial and external, respectively)are superposed.

Similar calculations can be made for parameters other than pH orhydronium concentration to determine the extent of their changes broughtabout by a transversal pressure being applied to the sensor element ofthe invention.

Determination of the Material Constants of the Gel

There are several parameters whose values can be prescribed a priori ormeasured directly. These include the dissociation constants of water,the polyelectrolyte gel, and the ¹⁹ F NMR indicator, the polymer volume,the material's bulk modulus, and the number and concentration ofionizable groups and the diffusivity of the indicator.

Also part of this invention is a kit comprising 1 to 100 sensor elementswhich may be sterilized and individually wrapped.

Also provided herein is a method of measuring in vivo contact stressapplied to an implanted pressure sensor element, comprising

(a) implanting the pressure sensor of the invention into a situs of asubject in need of such measurement;

(b) non-invasively subjecting the subject situs to a nuclear magneticresonance source effective to detect said NMR-detectible agent;

(c) obtaining the NMR spectrum of said agent;

(d) obtaining the chemical shifts from the spectrum;

(e) repeating steps (b) to (d) at least once at a desired time interval;

(f) comparing the chemical shifts obtained in step (d) at different timeintervals; and

(g) calculating the contact stress applied to said sensor element at adesired time from a correlation or calibration curve relating theobserved chemical shift to the normalized stress applied to the sensorelement.

The implantation of the sensor is conducted in accordance with knowntechniques in the art. These techniques should be sterile and conductedwith utmost care in order for the implanted device to be safely lodgedin a desired site. Care must also be exercised to close the implantationsite in complete sterility to ensure the safe long-term implantation ofthe present device.

There are various manners in which NMR spectra can be obtained and thoseare known in the art. Any of these techniques can be utilized forpracticing the present invention.

Steps (b) through (d) may be conducted as many times as desired in orderto obtain point comparisons in time or to follow the status of aparticular patient as needed. The time intervals may be as close asseconds apart and as far apart as days, weeks, months or years.

The sensor element of the invention may be removed after being implantedif it is determined that it is no longer necessary to follow up alocalized pathological development. The removal is undertaken bysurgical procedures known in the art.

The comparison of the chemical shifts obtained in step (d) of thepresent method may also be conducted by methods known in the art.

Thereafter, the contact stress applied to said sensor element at adesired time may be calculated from a correlation or calibration curverelating the observed chemical shift to the normalized stress applied tothe sensor element. One such example appears in the following table.

                  TABLE 1                                                         ______________________________________                                        Calibration Curve for Sensor Element of the Invention                                        Chemical Shift                                                                             Chemical Shift                                                   (ppm)        (ppm)                                             Normalized Stress                                                                            External     Interstitial                                      (σ/K)    Compartment  Compartment                                       ______________________________________                                        0.0000000000000000E + 00                                                                     4.391586151032058                                                                          4.522367371313221                                 1.4851485379040241E - 02                                                                     4.389266576446108                                                                          4.522135822243916                                 2.9702970758080482E - 02                                                                     4.386894352624341                                                                          4.521899367304929                                 4.4554457068443298E - 02                                                                     4.384468000324444                                                                          4.521657849898495                                 5.9405941516160965E - 02                                                                     4.381985991428452                                                                          4.521411106774711                                 7.4257425963878632E - 02                                                                     4.379446745475916                                                                          4.521158967532215                                 8.9108914136886597E - 02                                                                     4.376848627932138                                                                          4.520901254271981                                 0.1039603948593140                                                                           4.374189950936039                                                                          4.520637781481854                                 0.1188118830323219                                                                           4.371468963653133                                                                          4.520368354874742                                 0.1336633712053299                                                                           4.368683858416777                                                                          4.520092771774425                                 0.1485148519277573                                                                           4.365832764249117                                                                          4.519810820231108                                 0.1633663326501846                                                                           4.362913741142973                                                                          4.519522278193044                                 0.1782178282737732                                                                           4.359924778319357                                                                          4.519226913048662                                 0.1930693089962006                                                                           4.356863801837395                                                                          4.518924482067234                                 0.2079207897186279                                                                           4.353728653359045                                                                          4.518614729962164                                 0.2227722704410553                                                                           4.350517098645519                                                                          4.518297389362498                                 0.2376237660646439                                                                           4.347226817632364                                                                          4.517972179431002                                 0.2524752616882324                                                                           4.343855410462412                                                                          4.517638806023369                                 0.2673267424106598                                                                           4.340400387246609                                                                          4.517296960200471                                 0.2821782231330872                                                                           4.336859156613720                                                                          4.516946316575536                                 0.2970297038555145                                                                           4.333229031362762                                                                          4.516586533305093                                 0.3118811845779419                                                                           4.329507220321184                                                                          4.516217250662992                                 0.3267326653003693                                                                           4.325690823258127                                                                          4.515838089857938                                 0.3415841460227966                                                                           4.321776825490946                                                                          4.515448651756092                                 0.3564356565475464                                                                           4.317762084005046                                                                          4.515048514685721                                 0.3712871372699738                                                                           4.313643353808439                                                                          4.514637236174988                                 0.3861386179924011                                                                           4.309417233156625                                                                          4.514214346515224                                 0.4009900987148285                                                                           4.305080188718033                                                                          4.513779350192480                                 0.4158415794372559                                                                           4.300628540337361                                                                          4.513331723186497                                 0.4306930601596832                                                                           4.296058453292660                                                                          4.512870910895181                                 0.4455445408821106                                                                           4.291365930051765                                                                          4.512396325875326                                 0.4603960514068604                                                                           4.286546791696196                                                                          4.511907344384246                                 0.4752475321292877                                                                           4.281596707504355                                                                          4.511403307646468                                 0.4900990128517151                                                                           4.276511126975329                                                                          4.510883513032686                                 0.5049505233764648                                                                           4.271285296981563                                                                          4.510347213649311                                 0.5198019742965698                                                                           4.265914294031907                                                                          4.509793619319675                                 0.5346534848213196                                                                           4.260392894613094                                                                          4.509221880625205                                 0.5495049357414246                                                                           4.254715724710684                                                                          4.508631101427669                                 0.5643564462661743                                                                           4.248877068583150                                                                          4.508020315829301                                 0.5792078971862793                                                                           4.242871036324180                                                                          4.507388502016967                                 0.5940594077110291                                                                           4.236691360420059                                                                          4.506734556956984                                 0.6089109182357788                                                                           4.230331545800639                                                                          4.506057307660463                                 0.6237623691558838                                                                           4.223784782547839                                                                          4.505355497048957                                 0.6386138796806335                                                                           4.217043844250202                                                                          4.504627767374787                                 0.6534653306007385                                                                           4.210101252876398                                                                          4.503872671633165                                 0.6683168411254883                                                                           4.202949039623769                                                                          4.503088640630597                                 0.6831682920455933                                                                           4.195578943692932                                                                          4.502273996615836                                 0.6980198025703430                                                                           4.187982156364133                                                                          4.501426916178396                                 0.7128713130950928                                                                           4.180149497716269                                                                          4.500545439501254                                 0.7277227640151978                                                                           4.172071301813902                                                                          4.499627446211477                                 0.7425742745399475                                                                           4.163737282434994                                                                          4.498670626868532                                 0.7574257254600525                                                                           4.155136732789664                                                                          4.497672490153803                                 0.7722772359848022                                                                           4.146258198133166                                                                          4.496630310650084                                 0.7871286869049072                                                                           4.137089741839308                                                                          4.495541136573807                                 0.8019801974296570                                                                           4.127618595280836                                                                          4.494401728614706                                 0.8168317079544067                                                                           4.117831368878571                                                                          4.493208558533234                                 0.8316831588745117                                                                           4.107713894808518                                                                          4.491957760982756                                 0.8465346693992615                                                                           4.097251042341731                                                                          4.490645076161130                                 ______________________________________                                    

The method of the invention may also be practiced in a manner such thatsteps (d), (f) and (g) are computerized. This embodiment greatly speedsthe generation of data.

The sensor element of the invention may be implanted in a variety ofsites of a subject. Examples of these are between a tumor and itssurrounding tissue, a tumor and an adjacent bone, in an articulatedjoint, in a swollen tissue, between two swollen tissues, between amuscle and a fascia and the like.

Also provided herein is a method of measuring in vitro contact stressapplied to a pressure sensor element, comprising

(a) placing the stress sensor element of the invention in contact with abiological tissue in culture;

(b) non-invasively subjecting the biological tissue to a nuclearmagnetic resonance source effective to detect said NMR-detectible agent;

(c) obtaining the NMR spectrum of said agent;

(d) obtaining the chemical shifts from the spectrum;

(e) repeating steps (b) to (d) at least once at a desired time interval;

(f) comparing the chemical shifts obtained in step (d) at different timeintervals; and

(g) calculating the contact stress applied to said sensor element at adesired time from a correlation or calibration curve relating theobserved chemical shift to the normalized stress (σ/K) for the sensorelement.

In general the steps of this method may be practiced under the samecondition as those for the method of measuring in vivo contact stressdescribed above. However, in some cases different conditions may besuitable.

As in the previous case steps (d), (f) and (g) may be computerized inthe practice of this method.

In a particular embodiment of this method, the biological tissue is acell(s) which is (are) placed in contact with a sensor element andallowed to grow and proliferate in contact therewith to provide a layerof cells capable of applying a contact stress to the sensor element.Conditions under which the cells may be grown are known in the art andneed not be described herein. Also known in the art are growth media inwhich cells may proliferate and form layers in a culture.

Having now generally described this invention the same will be betterunderstood to certain specific examples, which are included herein forpurposes of illustration only and which are not intended to be limitingof the invention or any embodiment thereof, unless so specified.

EXAMPLES Example 1 Proton Spectra

FIGS. 5a and 5b depict the system used to demonstrate that an appliedstress can cause a measurable chemical shift during an in vitroexperiment with a phantom. The end of a 20 cm³ plastic syringe is sealedwith a paraffin tape. Holes are drilled through the rubber tamper sothat fluid can flow across it when the plunger is depressed. The syringeis first filled with 3.0 ml of polyacrylamide gel (15% by weight), 50.0mg of difluoromethylalanine hydrochloride (the ¹⁹ F NMR --pH indicator)and 0.1 NaOH and distilled, deionized water to bring the total volume to5.0 ml at pH 7.5. The cylindrical RF transmitting coil is first tuned.Then the syringe is placed in the coil and the entire assembly isinserted into the core of a 4.7 Tesla magnet (General Electric ***).Initially, no compressive force is applied to the plunger (correspondingto the configuration shown in FIG. 5a). Proton and ¹⁹ F NMR spectra areobtained by using Free Induction Decay (FID) after the magnetic fieldgradients are shimmed with the sample in place.

The same sample is then subjected to an applied compressive force ofapproximately 1.0 Newton (a mean stress of approximately 0.32 N/cm²) andthen allowed to equilibrate for about 1 hour. This test is depicted inFIG. 5b. Interstitial fluid from the gel flows into the reservoir abovethe sample. However, the total volume of polymer and solvent is constantin both tests. Proton and Fluorine NMR spectrum were again obtained forthe compressed sample.

FIGS. 6a and 6b show the proton spectra obtained from the uncompressedand compressed gel samples, respectively.

EXAMPLE 2 Fluorine Spectra

FIG. 7 shows the Fluorine NMR spectrum of the uncompressed sample whileFIG. 8 shows the Fluorine NMR spectrum of the compressed sample. Thefour sets of split peaks in the latter two figures are characteristicspectral lines of the Fluorine moiety, however, changes in the relativespacing between peaks (in ppm) reflect changes in ambient and internalpH.

EXAMPLE 3 Calibration curve of sensor element in accordance with theinvention.

Prior to implantation a sensor element in accordance with this inventiondescribed above is calibrated under the following conditions. Before thesensor is implanted, a calibration table can be generated by placing thegel sensor in a "phantom", applying a set of known loads, and measuringthe corresponding chemical shifts.

The results shown in the table below are obtained.

                                      TABLE 2                                     __________________________________________________________________________    Calibration of Sensor Element of Example 1                                    A        B      C     D      E     F     G                                    __________________________________________________________________________     3                                                                              AB system                                                                            quartet                                                                              analysis                                                       4                    Performance:                                                                         Resolution:                                                                         0.02408203                                                                          ppm                                   5                           Sensitivity                                                                         5.91715976                                                                          N/cm 2/ppm                            6                                                                              vr (MHz)                                                                             188.277038                                                            7                           spectral                                                                            2C-J                                        8       line number                                                                          (v - vr)/vr                                                                         v - vr line height                                                                         L2-L3 L2-L3                                 9              ppm   Hz     cm    Hz    ppm                                  10                                                                              uncompressed                                                                11       L4     -3.137                                                                              -590.62507                                                                           5.8   799.989134                                                                          4.249                                12       L3     -1.961                                                                              -369.21127                                                                           10                                               13       L2      2.288                                                                               430.777863                                                                          9                                                14       L1      3.467                                                                               652.756491                                                                           6.11                                            15                                                                            16       L4'    -3.423                                                                              -644.4723                                                                            5.5   695.871932                                                                          3.696                                17       L3'    -1.681                                                                              -316.4937                                                                            10.1                                             18       L2'     2.015                                                                               379.378232                                                                          10.1                                             19       L1'     3.746                                                                               705.285784                                                                           5.05                                            20                                                                            21                                                                              compressed                                                                  22       L4     - 3.203                                                                             -603.05135                                                                           6.3   768.170315                                                                          4.08                                 23       L3     -2.002                                                                              -376.93063                                                                           9.6                                              24       L2      2.078                                                                               391.239685                                                                           9.95                                            25       L1      3.265                                                                               614.724529                                                                          6.1                                              26                                                                            27       L4'    -3.487                                                                              -656.52203                                                                           5.1   668.760039                                                                          3.552                                28       L3'    -1.73 -325.71928                                                                           10.1                                             29       L2'     1.822                                                                               343.040763                                                                          10                                               30       L1'     3.538                                                                               666.12416                                                                            5.85                                            __________________________________________________________________________

I claim:
 1. A method of measuring in vivo contact stress applied to animplanted pressure sensor element which comprises:(a) implanting apressure sensor element into a situs of a subject, said pressure sensorelement having an NMR spectrum which changes in response to pressuresapplied to said pressure sensor element; (b) non-invasively subjectingthe subject situs to a nuclear magnetic resonance source to obtain anNMR spectrum of said pressure sensor element; and (c) determining invivo contact stress applied to said pressure sensor element from saidNMR spectrum obtained in step (b).
 2. The method of claim 1, whereinthepressure sensor element is implanted between a tumor and its surroundingtissue.
 3. The method of claim 1, whereinthe pressure sensor element isimplanted between a tumor and an adjacent bone.
 4. The method of claim1, whereinthe pressure sensor element is implanted in an articulatedjoint.
 5. The method of claim 1, whereinthe pressure sensor element isimplanted into a swollen tissue.
 6. The method of claim 1, whereinthepressure sensor element is implanted between two swollen tissues.
 7. Themethod of claim 1, whereinthe pressure sensor element is implantedbetween a muscle and a fascia.
 8. A method of monitoring in vivo contactstress applied to an implanted pressure sensor element whichcomprises:(a) implanting a pressure sensor element into a situs of asubject, said pressure sensor element having an NMR spectrum whichchanges in response to pressure applied to said pressure sensor element;(b) non-invasively subjecting the subject situs to a nuclear magneticresonance source at a first time, t₁, to obtain an NMR spectrum of saidpressure sensor element at said first time, t₁ ; (c) determining in vivocontact stress applied to said pressure sensor element at said firsttime, t₁, from said NMR spectrum obtained in step (b); (d)non-invasively subjecting the subject situs to a nuclear magneticresonance source at a second time, t₂, to obtain an NMR spectrum of saidpressure sensor element at said second time, t₂, wherein t₂ >t₁ ; (e)determining in vivo contact stress applied to said pressure sensorelement at said second time, t₂, from said NMR spectrum obtained in step(c); and (f) comparing said in vivo contact stress obtained in steps (c)and (e).
 9. The method of claim 8, whereinthe pressure sensor element isimplanted between a tumor and its surrounding tissue.
 10. The method ofclaim 8, whereinthe pressure sensor element is implanted between a tumorand an adjacent bone.
 11. The method of claim 8, whereinthe pressuresensor element is implanted in an articulated joint.
 12. The method ofclaim 8, whereinthe pressure sensor element is implanted into a swollentissue.
 13. The method of claim 8, whereinthe pressure sensor element isimplanted between two swollen tissues.
 14. The method of claim 8,whereinthe pressure sensor element is implanted between a muscle and afascia.
 15. The method of claim 8, wherein the difference between t₂ andt₁ ranges from several seconds to several years.